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8: Klamath and The Modoc Plateau
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Learning Objectives
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Identify the physical characteristics of the Klamath Mountains and Modoc Plateau provinces.
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Explore the cultural significance of the region, as well as the peoples who called this province their home over time.
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Explain the geology and formation of the volcanism historically and presently found within the Modoc Plateau.
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8.1: Introduction
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This unit explores the Klamath Mountain and Modoc Plateau provinces. The Klamath Mountains, spanning northwestern California and southwestern Oregon, are part of the Pacific Coast Ranges and feature diverse geology and climate fostering rich biodiversity. The Modoc Plateau, located in northeastern California, is characterized by volcanic tablelands with faults, lakes, and streams. Both regions boast unique geological and biological significance, supporting a range of flora and fauna.
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8.2: Klamath Mountains
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The Klamath Mountains, originally low and smooth, rose over time, resulting in deep canyons like the Klamath River canyon. The landscape shaped by uplift and erosion now features rugged mountains and valleys, with distinct ranges like the Salmon and Siskiyou Mountains. The region???s geology is a result of ancient island arcs and continental fragments, rich with gold-bearing gravels, leading to historical mining. Mount Shasta, a prominent volcano here, has a complex formation history.
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8.3: Modoc Plateau
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The Modoc Plateau, located in northeastern California, is characterized by a diverse geography and ecology, comprising the Modoc Plateau and Southern Cascades. This region, with elevations ranging from 3,000 to over 14,000 feet, is rich in wildlife and has unique aquatic communities. It features significant volcanic history, notably seen in Lava Beds National Monument, which contains numerous volcanic formations and the largest concentration of lava tubes in North America.
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8.4: Climatic Features
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The region's climate varies significantly; the coastal areas are extremely wet with mild temperatures, while inland areas experience less precipitation, warmer summers, and colder winters. Higher mountains present semi-arctic conditions. There is a notable vertical range for plants and trees, such as the madrone and Spanish bayonet, depending on slope exposure and conditions. Rainfall is lighter on the eastern edge of the district.


8.3: Seismic Waves
The point on a fault within earth’s crust where the fracturing begins and most slippage occurs is called the focus of the earthquake. Another name for it is the hypocenter. The point on the earth’s surface directly above the focus is the epicenter. The epicenter is not where the earthquake originated. Earthquakes originate within the earth. The epicenter is the point on the surface of the earth directly above where the earthquake originated.
When an earthquake occurs, some of the energy it releases is turned into heat within the earth. Some of the energy is expended in breaking and permanently deforming the rocks and minerals along the fault. The rest of the energy, which is most of the energy, is radiated from the focus of the earthquake in the form of seismic waves.
Seismic waves fall into two general categories: body waves, which travel through the interior of the earth, and surface waves, which travel only at the earth’s surface.
BODY WAVES
There are two types of body waves: P-waves and S-waves. The P in P-waves stands for primary, because these are the fastest seismic waves and are the first to be detected once an earthquake has occurred. P-waves travel through the earth’s interior many times faster than the speed of a jet airplane, taking only a few minutes to travel across the earth.
P-waves are predominantly compressional waves. As a P-wave passes, material compresses in the same direction the wave is moving, and then extends back to its original thickness once the wave has passed. The speed at which P-waves travel through material is determined by:
- rigidity—how strongly the material resists being bent sideways and is able to straighten itself out once the shearing force has passed – the more rigid the material, the faster the P-waves
- compressibility—how much the material can be compressed into a smaller volume and then recover its previous volume once the compressing force has passed; the more compressible the material, the faster the P-waves
- density—how much mass the material contains in a unit of volume; the greater the density of the material, the slower the P-waves
The animations below show P-waves propogating across a plane (left) and from a point source (right). They are from Wikipedia.org/wiki/P-wave uploaded November, 2006 by Christophe Dang Ngoc Chan.
P-waves travel through liquids and gases as well as through solids. Although liquids and gases have zero rigidity, they have compressibility, which enables them to transmit P-waves. Sound waves are P-waves moving through the air.
Because the earth’s mantle becomes more rigid and compressible as the depth below the asthenosphere increases, P-waves travel faster as they go deeper in the mantle. The density of the mantle also increases with depth below the asthenosphere. The higher density reduces the speed of seismic waves. However, the effects of increased rigidity and compressibility in the deep mantle are much greater than the effect of the increased density.
| P-waves travel through materials with rigidity and/or compressiblity, and density | |
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| greater rigidity | faster P-waves |
| greater compressibility | faster P-waves |
| greater density | slower P-waves |
The S in S-waves stands for secondary, because they are the second-fastest seismic waves and the second type to be detected once an earthquake has occurred. Although S-waves are slower than P-waves, they still travel fast, over half the speed of P-waves, moving at thousands of kilometers per hour through the earth’s crust and mantle.
S-waves are shear waves (though that is not what the S stands for). They move by material flexing or deforming sideways (shearing) from the direction of wave travel, and then returning to the original shape once the wave passes. The speed at which S-waves travel through material is determined only by:
- rigidity — how strongly the material resists being bent sideways and is able to straighten itself out once the shearing force has passed – the more rigid the material, the faster the S-waves
- density — how much mass the material contains in a unit of volume – the greater the density of the material, the slower the S-waves
The animations below show S-waves propogating across a plane (left) and from a point source (right). They are from Wikipedia.org/wiki/S-wave uploaded November, 2006 by Christophe Dang Ngoc Chan.
S-waves can travel only through solids, because only solids have rigidity. S-waves cannot travel through liquids or gases.
Because the earth’s mantle becomes more rigid as its depth below the asthenosphere increases, S-waves travel faster as they go deeper in the mantle. The density of the mantle also increases at greater depth, which has the effect of reducing the speed of seismic waves, but the increase in rigidity is much greater than the increase in density, so S-waves speed up as they get deeper in the mantle, in spite of the increased density.
| S-waves travel through materials with rigidity and density | |
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| greater rigidity | faster S-waves |
| greater density | slower S-waves |
SURFACE WAVES
There are two types of surface waves, Rayleigh waves and Love waves. Rayleigh waves are named after Lord Rayleigh (John Strutt), an English aristocrat who, in his work as a scientist and mathematician, developed a detailed mathematical accounting of the type of surface wave named after him. Rayleigh waves are set off by the combined effect of P- and S-waves on the earth’s surface. Rayleigh waves are sometimes called rolling waves. In Rayleigh waves the surface of the earth rises up and sinks down in crests and troughs, similar to waves on the surface of water. People who are outdoors during a major earthquake commonly see Rayleigh waves moving across the surface of the earth, and can feel the ground rising and falling as the waves pass beneath them.
Love waves, sometimes called L-waves, are named after Augustus Love, an English mathematician and physicist who first modeled them mathematically. Love waves involve the surface shearing sideways and then returning to its original form as each wave passes.
All surface waves travel slower than body waves and Rayleigh waves are slower than Love waves.
REFLECTION QUESTIONS
- What skill does this content help you develop?
- What are the key topics covered in this content?
- How can the content in this section help you demonstrate mastery of a specific skill?
- What questions do you have about this content?
Contributors and Attributions
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Original content from Kimberly Schulte (Columbia Basin College) and supplemented by Lumen Learning . The content on this page is copyrighted under a Creative Commons Attribution 4.0 International license.


In this section you will be introduced to the molecular orbital diagrams of several homonuclear diatomic molecules. Homonuclear diatomic molecules are molecules made of exactly two identical atoms, and they are relatively simple.
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5.2.1: Molecular Orbitals
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There are several cases where our more elementary models of bonding (like Lewis Theory and Valence Bond Theory) fail to predict the actual molecular properties and reactivity. A classic example is the case of O₂ and its magnetic properties. At very cold temperatures, O₂ is attracted to a magnetic field, and thus it must be paramagnetic (unpaired electrons give rise to magnetism, see video). However, both its Lewis structure and Valance Bond Theory predict that O₂ is diamagnetic.
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5.2.2: Orbital Mixing
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Orbitals of compatible symmetry can combine, or mix, even when they have different energies. When sets of orbitals mix, it has the effect of decreasing the energy of the lower-energy set and increasing the energy of the higher-energy set.
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5.2.3: Diatomic Molecules of the First and Second Periods
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5.2.4: Photoelectron Spectroscopy
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3: Linear Programming - A Geometric Approach
In this chapter, you will learn to:
- Solve linear programming problems that maximize the objective function.
- Solve linear programming problems that minimize the objective function.
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- 3.1: Maximization Applications
- Application problems in business, economics, and social and life sciences often ask us to make decisions on the basis of certain conditions. The conditions or constraints often take the form of inequalities. In this section, we will begin to formulate, analyze, and solve such problems, at a simple level, to understand the many components of such a problem.
Thumbnail: A pictorial representation of a simple linear program with two variables and six inequalities. The set of feasible solutions is depicted in yellow and forms a polygon, a 2-dimensional polytope. The linear cost function is represented by the red line and the arrow: The red line is a level set of the cost function, and the arrow indicates the direction in which we are optimizing. (CC0; Ylloh via Wikipedia)


5.5: The History of Instructional Technology in Education
References
Rumble, G. (2003). Modeling the cost and economics of distance education. Handbook of Distance Education. New Jersey: Lawrence Erlbaum Associates.
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In the early ages, before formal schools, family members educated younger members with one-to-one coaching and mentoring. Early instructional technologies were sticks to draw on the ground and rocks to draw on walls. Information was not recorded permanently. With the invention of paper and the printing press, information was recorded, and learners could refer to documents as needed for learning. The paper revolution was followed much later by the invention of computer hardware and the software that makes computers do what we want, including developing electronic learning materials.
In the early 1960s, these learning materials were designed and developed on mainframe computers. In the 1970s, computer-based training systems used minicomputers to teach. With the invention of the microcomputer in the late 1970s and early 1980s educators and learners had more control over the design and delivery of learning materials. As learners determined for themselves what they wanted to learn, the instructor’s role changed from that of a presenter of information to that of a facilitator. The microcomputer revolutionized the way educational materials were developed and delivered. The instructor was able to design learning materials using authoring systems, and learners were able to learn when and where they wanted.
Rumble (2003) identified four generations of distance education systems: correspondence systems; educational broadcasting systems; multimedia distance education systems; and online distance education systems. In early distance education learning materials were mailed to learners and the learners mailed assignments back to the instructor. The first attempt to use computers for instruction was by the military, who designed instruction to train military staff. About the same time, educational institutions started to use broadcast television to deliver instruction to learners. With the invention of the microcomputer in the 1970s, there was a shift to microcomputer-based learning systems. Because the different microcomputer systems then in use did not communicate with each other, there was limited flexibility in developing and sharing learning materials. Also, the early microcomputer systems did not provide features such as audio, video, and special effects. As instructional technology improved, educators developed learning materials in less time and with more control over the product.
Until the late 1970s, educational institutions used face-to-face classroom instruction. This was followed by a shift to a more individualized format using self-study workbooks, videotapes, and computer software. As technology advanced, the group-based classroom mode shifted to the one-to-one mode of delivery. The combination of the Internet and mobile technology has moved elearning to the next generation, allowing educators to design and deliver learning materials for learners living in remote locations, or who cannot attend face-to-face schools for other reasons. The available computing power of these technologies allows educators to better meet the needs of individual learners.
Rumble, G. (2003). Modeling the cost and economics of distance education. Handbook of Distance Education. New Jersey: Lawrence Erlbaum Associates.


8.6: Viewing a Worksheet
Learning Objectives
- Change page layout orientation
- Change margins
Now that we’ve learned a variety of applications and tips for using Excel, this final section will focus on options for viewing and printing worksheets. There are two important considerations here: the way the page is oriented and the margins. Both can be adjusted with just a few clicks in Excel.
Page Layout Orientation
Just like in Word, by default Excel is set to a portrait orientation (which means it is taller than it is wide). Depending on how many columns your worksheet has though, this may not be the best orientation. The other option is the landscape orientation, where the page prints left to right along the long side of a page.
- Click on the Page Layout tab
- Within the Page Setup group you will find the Orientation dropdown.
- Click the arrow to access the menu and then select the orientation you want. Again, by default Excel is set to portrait, so you will generally use this to switch to landscape.
Practice Question
Margins
Sometimes your worksheet will not quite fit within the standard margins for a printed page. This can occur in portrait or landscape orientation, and the easiest fix could be to print closer to the physical edge of the paper. At other times, for visual reasons you may want your margins to be a bit larger than normal. In this case your printed worksheet would be farther away from the edge of the paper. This can be helpful if you are making a binder and need to punch holes into the edge of the sheet.
In either case, to change margins in Excel:
- Click on the Page Layout tab
- Within the Page Setup group you will find the Margins dropdown.
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Click the arrow to access the menu and then select the margins you want.
- By default, the page is at Normal margins.
- Wide margins will move the printed area away from the edge of the paper.
- Narrow margins will move the printed area toward the edge of the paper.
You may also set custom margins if you need to.
Practice Question
Contributors and Attributions
- Viewing a Worksheet. Authored by : Shelli Carter. Provided by : Lumen Learning. License : CC BY: Attribution
- Portrait vs landscape. Authored by : Sam Beebe. Located at : https://www.flickr.com/photos/sbeebe/8113091175 . License : CC BY: Attribution


1.6: Outliers
At the end of this section you should be able to answer the following questions:
- Explain the differences between a spurious and non-spurious outlier.
- Identify the level of z score for a response that typically indicates an outlier.
One of the major concerns when analysing data is the effect that outliers – which are unusually high or low data points – can have on the overall results. For example, if you were asking everyday people how many cups of coffee they consume a day, and most of the responses were between zero to four, that would be a normal spread of responses.
However, if you had one participant who responded that they consumed 17 cups of coffee a day, we would consider this response to be an outlier when compared to the rest of the participants. We could assume this participant has either a caffeine problem or they have incorrectly entered their response. Either way, this response will increase the mean for this particular sample, without being representative of the average coffee drinker.
There are a number of ways to statistically identify outliers in your data set. Participant responses to any variable can be transformed to a “z score,” which is a basic transformation allowing you to compare responses across cases to a standardized response, which has a mean of 0 and standard deviation of 1. If a response has a z score of greater than +/- 3.3, it is to be considered to be an outlier. Another way is to graph the data using a box plot or bar graph, and visually identify the outliers. We will run through these options in greater detail later.
Normally, when you find outliers you can do two things: include them in the final analysis if you consider the outliers to be non-spurious , or you can remove them if the outliers have occurred for spurious reasons, meaning that they do not reflect accurate responses. If the outliers don’t make sense in the context of the question, or are extreme without any potential justification, is a good idea to consider these as spurious responses and just remove them from the analysis. However, if you do find some responses that make sense or are only slightly outside the acceptable z score (+/-3.3), it may be worth considering them to be non-spurious outliers and keeping them for analysis.


8.1: Introduction to Popular Music in the United States
Popular music is by definition music that is disseminated widely. As such, it has been particularly significant with the twentieth-century proliferation of recording technologies and mass media. Sometimes we may forget that it was not until the 1920s that recording and playback technology allowed for the spread of music through records. To become popular before that time, a tune had to be spread by word of mouth, by traveling performers, and by music notation, which might ap- pear in a music magazine or newspaper or in sheet music that could be bought at general stores, catalogs, and music stores.
Today the success of a popular music artist is most often measured by how many songs they sell. In the past, that meant record and CD sales, but today it essentially means numbers of downloads. Recording industry executives determine which artists to record and distribute based almost entirely on their perceived ability to sell units. Most popular music today is sold by downloading it to an electronic device, though CDs are still manufactured and distributed.
Popular music is also often thought of as ephemeral, that is, as remaining in the consciousness of a group of people for a limited time. For this chapter, we have chosen popular music that has either transcended that boundary or that was so important in or exemplary of its time and place that its discussion helps us understand music, history, and culture more broadly. It is, however, but a sampling of a huge body of popular music that exists in the United States since roughly the Colonial period. As you listen to these examples, perhaps you can think of similar examples of popular music that you know.


5.7: Kinetic-Molecular Theory
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Learning Objectives
- To understand the significance of the kinetic molecular theory of gases.
The laws that describe the behavior of gases were well established long before anyone had developed a coherent model of the properties of gases. In this section, we introduce a theory that describes why gases behave the way they do. The theory we introduce can also be used to derive laws such as the ideal gas law from fundamental principles and the properties of individual particles.
A Molecular Description
The kinetic molecular theory of gases explains the laws that describe the behavior of gases. Developed during the mid-19th century by several physicists, including the Austrian Ludwig Boltzmann (1844–1906), the German Rudolf Clausius (1822–1888), and the Englishman James Clerk Maxwell (1831–1879), who is also known for his contributions to electricity and magnetism, this theory is based on the properties of individual particles as defined for an ideal gas and the fundamental concepts of physics. Thus the kinetic molecular theory of gases provides a molecular explanation for observations that led to the development of the ideal gas law. The kinetic molecular theory of gases is based on the following five postulates:
five postulates of Kinetic Molecular Theory
- A gas is composed of a large number of particles called molecules (whether monatomic or polyatomic) that are in constant random motion.
- Because the distance between gas molecules is much greater than the size of the molecules, the volume of the molecules is negligible.
- Intermolecular interactions, whether repulsive or attractive, are so weak that they are also negligible.
- Gas molecules collide with one another and with the walls of the container, but these collisions are perfectly elastic; that is, they do not change the average kinetic energy of the molecules.
- The average kinetic energy of the molecules of any gas depends on only the temperature, and at a given temperature, all gaseous molecules have exactly the same average kinetic energy.
Although the molecules of real gases have nonzero volumes and exert both attractive and repulsive forces on one another, for the moment we will focus on how the kinetic molecular theory of gases relates to the properties of gases we have been discussing. In the following sections, we explain how this theory must be modified to account for the behavior of real gases.
Postulates 1 and 4 state that gas molecules are in constant motion and collide frequently with the walls of their containers. The collision of molecules with their container walls results in a momentum transfer (impulse) from molecules to the walls (Figure \(\PageIndex{2}\)).
The momentum transfer to the wall perpendicular to \(x\) axis as a molecule with an initial velocity \(u_x\) in \(x\) direction hits is expressed as:
\[\Delta p_x=2mu_x \label{10.7.1} \]
The collision frequency , a number of collisions of the molecules to the wall per unit area and per second, increases with the molecular speed and the number of molecules per unit volume.
\[f\propto (u_x) \times \Big(\dfrac{N}{V}\Big) \label{10.7.2} \]
The pressure the gas exerts on the wall is expressed as the product of impulse and the collision frequency.
\[P\propto (2mu_x)\times(u_x)\times\Big(\dfrac{N}{V}\Big)\propto \Big(\dfrac{N}{V}\Big)mu_x^2 \label{10.7.3} \]
At any instant, however, the molecules in a gas sample are traveling at different speed. Therefore, we must replace \(u_x^2\) in the expression above with the average value of \(u_x^2\), which is denoted by \(\overline{u_x^2}\). The overbar designates the average value over all molecules.
The exact expression for pressure is given as :
\[P=\dfrac{N}{V}m\overline{u_x^2} \label{10.7.4} \]
Finally, we must consider that there is nothing special about \(x\) direction. We should expect that
\[\overline{u_x^2}= \overline{u_y^2}=\overline{u_z^2}=\dfrac{1}{3}\overline{u^2}. \nonumber \]
Here the quantity \(\overline{u^2}\) is called the mean-square speed defined as the average value of square-speed (\(u^2\)) over all molecules. Since
\[u^2=u_x^2+u_y^2+u_z^2 \nonumber \]
for each molecule, then
\[\overline{u^2}=\overline{u_x^2}+\overline{u_y^2}+\overline{u_z^2}. \nonumber \]
By substituting \(\dfrac{1}{3}\overline{u^2}\) for \(\overline{u_x^2}\) in the expression above, we can get the final expression for the pressure:
\[P=\dfrac{1}{3}\dfrac{N}{V}m\overline{u^2} \label{10.7.5} \]
Because volumes and intermolecular interactions are negligible, postulates 2 and 3 state that all gaseous particles behave identically, regardless of the chemical nature of their component molecules. This is the essence of the ideal gas law, which treats all gases as collections of particles that are identical in all respects except mass. Postulate 2 also explains why it is relatively easy to compress a gas; you simply decrease the distance between the gas molecules.
Postulate 5 provides a molecular explanation for the temperature of a gas. Postulate 5 refers to the average translational kinetic energy of the molecules of a gas \((\overline{e_K})\), which can be represented as and states that at a given Kelvin temperature \((T)\) , all gases have the same value of
\[\overline{e_K}=\dfrac{1}{2}m\overline{u^2}=\dfrac{3}{2}\dfrac{R}{N_A}T \label{10.7.6} \]
where \(N_A\) is the Avogadro's constant. The total translational kinetic energy of 1 mole of molecules can be obtained by multiplying the equation by \(N_A\):
\[N_A\overline{e_K}=\dfrac{1}{2}M\overline{u^2}=\dfrac{3}{2}RT \label{10.7.7} \]
where \(M\) is the molar mass of the gas molecules and is related to the molecular mass by \(M=N_Am\). By rearranging the equation, we can get the relationship between the root-mean square speed (\(u_{\rm rms}\)) and the temperature. The rms speed (\(u_{\rm rms}\)) is the square root of the sum of the squared speeds divided by the number of particles:
\[u_{\rm rms}=\sqrt{\overline{u^2}}=\sqrt{\dfrac{u_1^2+u_2^2+\cdots u_N^2}{N}} \label{10.7.8} \]
where \(N\) is the number of particles and \(u_i\) is the speed of particle \(i\).
The relationship between \(u_{\rm rms}\) and the temperature is given by:
\[u_{\rm rms}=\sqrt{\dfrac{3RT}{M}} \label{10.7.9} \]
In Equation \(\ref{10.7.9}\), \(u_{\rm rms}\) has units of meters per second; consequently, the units of molar mass \(M\) are kilograms per mole, temperature \(T\) is expressed in kelvins, and the ideal gas constant \(R\) has the value 8.3145 J/(K•mol). Equation \(\ref{10.7.9}\) shows that \(u_{\rm rms}\) of a gas is proportional to the square root of its Kelvin temperature and inversely proportional to the square root of its molar mass. The root mean-square speed of a gas increase with increasing temperature. At a given temperature, heavier gas molecules have slower speeds than do lighter ones.
The rms speed and the average speed do not differ greatly (typically by less than 10%). The distinction is important, however, because the rms speed is the speed of a gas particle that has average kinetic energy. Particles of different gases at the same temperature have the same average kinetic energy, not the same average speed. In contrast, the most probable speed (vp) is the speed at which the greatest number of particles is moving. If the average kinetic energy of the particles of a gas increases linearly with increasing temperature, then Equation \(\ref{10.7.8}\) tells us that the rms speed must also increase with temperature because the mass of the particles is constant. At higher temperatures, therefore, the molecules of a gas move more rapidly than at lower temperatures, and vp increases.
At a given temperature, all gaseous particles have the same average kinetic energy but not the same average speed.
Example \(\PageIndex{1}\)
The speeds of eight particles were found to be 1.0, 4.0, 4.0, 6.0, 6.0, 6.0, 8.0, and 10.0 m/s. Calculate their average speed (\(v_{\rm av}\)) root mean square speed (\(v_{\rm rms}\)), and most probable speed (\(v_{\rm m}\)).
Given: particle speeds
Asked for: average speed (\(v_{\rm av}\)), root mean square speed (\(v_{\rm rms}\)), and most probable speed (\(v_{\rm m}\))
Strategy:
Use Equation \(\ref{10.7.6}\) to calculate the average speed and Equation \(\ref{10.7.8}\) to calculate the rms speed. Find the most probable speed by determining the speed at which the greatest number of particles is moving.
Solution:
The average speed is the sum of the speeds divided by the number of particles:
\[v_{\rm av}=\rm\dfrac{(1.0+4.0+4.0+6.0+6.0+6.0+8.0+10.0)\;m/s}{8}=5.6\;m/s \nonumber \]
The rms speed is the square root of the sum of the squared speeds divided by the number of particles:
\[v_{\rm rms}=\rm\sqrt{\dfrac{(1.0^2+4.0^2+4.0^2+6.0^2+6.0^2+6.0^2+8.0^2+10.0^2)\;m^2/s^2}{8}}=6.2\;m/s \nonumber \]
The most probable speed is the speed at which the greatest number of particles is moving. Of the eight particles, three have speeds of 6.0 m/s, two have speeds of 4.0 m/s, and the other three particles have different speeds. Hence \(v_{\rm m}=6.0\) m/s. The \(v_{\rm rms}\) of the particles, which is related to the average kinetic energy, is greater than their average speed.
Boltzmann Distributions
At any given time, what fraction of the molecules in a particular sample has a given speed? Some of the molecules will be moving more slowly than average, and some will be moving faster than average, but how many in each situation? Answers to questions such as these can have a substantial effect on the amount of product formed during a chemical reaction. This problem was solved mathematically by Maxwell in 1866; he used statistical analysis to obtain an equation that describes the distribution of molecular speeds at a given temperature. Typical curves showing the distributions of speeds of molecules at several temperatures are displayed in Figure \(\PageIndex{3}\). Increasing the temperature has two effects. First, the peak of the curve moves to the right because the most probable speed increases. Second, the curve becomes broader because of the increased spread of the speeds. Thus increased temperature increases the value of the most probable speed but decreases the relative number of molecules that have that speed. Although the mathematics behind curves such as those in Figure \(\PageIndex{3}\) were first worked out by Maxwell, the curves are almost universally referred to as Boltzmann distributions, after one of the other major figures responsible for the kinetic molecular theory of gases.
The Relationships among Pressure, Volume, and Temperature
We now describe how the kinetic molecular theory of gases explains some of the important relationships we have discussed previously.
- Pressure versus Volume : At constant temperature, the kinetic energy of the molecules of a gas and hence the rms speed remain unchanged. If a given gas sample is allowed to occupy a larger volume, then the speed of the molecules does not change, but the density of the gas (number of particles per unit volume) decreases, and the average distance between the molecules increases. Hence the molecules must, on average, travel farther between collisions. They therefore collide with one another and with the walls of their containers less often, leading to a decrease in pressure. Conversely, increasing the pressure forces the molecules closer together and increases the density, until the collective impact of the collisions of the molecules with the container walls just balances the applied pressure.
- Volume versus Temperature : Raising the temperature of a gas increases the average kinetic energy and therefore the rms speed (and the average speed) of the gas molecules. Hence as the temperature increases, the molecules collide with the walls of their containers more frequently and with greater force. This increases the pressure, unless the volume increases to reduce the pressure, as we have just seen. Thus an increase in temperature must be offset by an increase in volume for the net impact (pressure) of the gas molecules on the container walls to remain unchanged.
- Pressure of Gas Mixtures : Postulate 3 of the kinetic molecular theory of gases states that gas molecules exert no attractive or repulsive forces on one another. If the gaseous molecules do not interact, then the presence of one gas in a gas mixture will have no effect on the pressure exerted by another, and Dalton’s law of partial pressures holds.
Example \(\PageIndex{2}\)
The temperature of a 4.75 L container of N 2 gas is increased from 0°C to 117°C. What is the qualitative effect of this change on the
- average kinetic energy of the N 2 molecules?
- rms speed of the N 2 molecules?
- average speed of the N 2 molecules?
- impact of each N 2 molecule on the wall of the container during a collision with the wall?
- total number of collisions per second of N 2 molecules with the walls of the entire container?
- number of collisions per second of N 2 molecules with each square centimeter of the container wall?
- pressure of the N 2 gas?
Given: temperatures and volume
Asked for: effect of increase in temperature
Strategy:
Use the relationships among pressure, volume, and temperature to predict the qualitative effect of an increase in the temperature of the gas.
Solution:
- Increasing the temperature increases the average kinetic energy of the N 2 molecules.
- An increase in average kinetic energy can be due only to an increase in the rms speed of the gas particles.
- If the rms speed of the N 2 molecules increases, the average speed also increases.
- If, on average, the particles are moving faster, then they strike the container walls with more energy.
- Because the particles are moving faster, they collide with the walls of the container more often per unit time.
- The number of collisions per second of N 2 molecules with each square centimeter of container wall increases because the total number of collisions has increased, but the volume occupied by the gas and hence the total area of the walls are unchanged.
- The pressure exerted by the N 2 gas increases when the temperature is increased at constant volume, as predicted by the ideal gas law.
Exercise \(\PageIndex{2}\)
A sample of helium gas is confined in a cylinder with a gas-tight sliding piston. The initial volume is 1.34 L, and the temperature is 22°C. The piston is moved to allow the gas to expand to 2.12 L at constant temperature. What is the qualitative effect of this change on the
- average kinetic energy of the He atoms?
- rms speed of the He atoms?
- average speed of the He atoms?
- impact of each He atom on the wall of the container during a collision with the wall?
- total number of collisions per second of He atoms with the walls of the entire container?
- number of collisions per second of He atoms with each square centimeter of the container wall?
- pressure of the He gas?
- Answer a
-
no change
- Answer b
-
no change
- Answer c
-
no change
- Answer d
-
no change
- Answer e
-
decreases
- Answer f
-
decreases
- Answer g
-
decreases
Summary
- The kinetic molecular theory of gases provides a molecular explanation for the observations that led to the development of the ideal gas law.
- Average kinetic energy: \[\overline{e_K}=\dfrac{1}{2}m{u_{\rm rms}}^2=\dfrac{3}{2}\dfrac{R}{N_A}T n\nonumber \]
- Root mean square speed: \[u_{\rm rms}=\sqrt{\dfrac{u_1^2+u_2^2+\cdots u_N^2}{N}} \nonumber \]
- Kinetic molecular theory of gases: \[u_{\rm rms}=\sqrt{\dfrac{3RT}{M}} \nonumber \]
The behavior of ideal gases is explained by the kinetic molecular theory of gases . Molecular motion, which leads to collisions between molecules and the container walls, explains pressure, and the large intermolecular distances in gases explain their high compressibility. Although all gases have the same average kinetic energy at a given temperature, they do not all possess the same root mean square (rms) speed ( v rms ) . The actual values of speed and kinetic energy are not the same for all particles of a gas but are given by a Boltzmann distribution , in which some molecules have higher or lower speeds (and kinetic energies) than average.


10.2B: The Mitotic Phase and the G0 Phase
- Describe the events that occur at the different stages of mitosis
The Mitotic Phase
The mitotic phase is a multistep process during which the duplicated chromosomes are aligned, separated, and move into two new, identical daughter cells. The first portion of the mitotic phase is called karyokinesis or nuclear division. The second portion of the mitotic phase, called cytokinesis, is the physical separation of the cytoplasmic components into the two daughter cells.
Karyokinesis (Mitosis)
Karyokinesis, also known as mitosis, is divided into a series of phases (prophase, prometaphase, metaphase, anaphase, and telophase) that result in the division of the cell nucleus.
During prophase, the “first phase,” the nuclear envelope starts to dissociate into small vesicles. The membranous organelles (such as the Golgi apparatus and endoplasmic reticulum) fragment and disperse toward the periphery of the cell. The nucleolus disappears and the centrosomes begin to move to opposite poles of the cell. Microtubules that will eventually form the mitotic spindle extend between the centrosomes, pushing them farther apart as the microtubule fibers lengthen. The sister chromatids begin to coil more tightly with the aid of condensin proteins and become visible under a light microscope.
During prometaphase, the “first change phase,” many processes that began in prophase continue to advance. The remnants of the nuclear envelope fragment. The mitotic spindle continues to develop as more microtubules assemble and stretch across the length of the former nuclear area. Chromosomes become more condensed and discrete. Each sister chromatid develops a protein structure called a kinetochore in the centromeric region. The proteins of the kinetochore attract and bind mitotic spindle microtubules.
During metaphase, the “change phase,” all the chromosomes are aligned on a plane called the metaphase plate, or the equatorial plane, midway between the two poles of the cell. The sister chromatids are still tightly attached to each other by cohesin proteins. At this time, the chromosomes are maximally condensed.
During anaphase, the “upward phase,” the cohesin proteins degrade, and the sister chromatids separate at the centromere. Each chromatid, now called a chromosome, is pulled rapidly toward the centrosome to which its microtubule is attached. The cell becomes visibly elongated (oval shaped) as the polar microtubules slide against each other at the metaphase plate where they overlap.
During telophase, the “distance phase,” the chromosomes reach the opposite poles and begin to decondense (unravel), relaxing into a chromatin configuration. The mitotic spindles are depolymerized into tubulin monomers that will be used to assemble cytoskeletal components for each daughter cell. Nuclear envelopes form around the chromosomes and nucleosomes appear within the nuclear area.
Cytokinesis
Cytokinesis, or “cell motion,” is the second main stage of the mitotic phase during which cell division is completed via the physical separation of the cytoplasmic components into two daughter cells. Division is not complete until the cell components have been apportioned and completely separated into the two daughter cells. Although the stages of mitosis are similar for most eukaryotes, the process of cytokinesis is quite different for eukaryotes that have cell walls, such as plant cells.
In cells such as animal cells, which lack cell walls, cytokinesis follows the onset of anaphase. A contractile ring composed of actin filaments forms just inside the plasma membrane at the former metaphase plate. The actin filaments pull the equator of the cell inward, forming a fissure. This fissure or “crack” is called the cleavage furrow. The furrow deepens as the actin ring contracts; eventually the membrane is cleaved in two.
In plant cells, a new cell wall must form between the daughter cells. During interphase, the Golgi apparatus accumulates enzymes, structural proteins, and glucose molecules prior to breaking into vesicles and dispersing throughout the dividing cell. During telophase, these Golgi vesicles are transported on microtubules to form a phragmoplast (a vesicular structure) at the metaphase plate. There, the vesicles fuse and coalesce from the center toward the cell walls; this structure is called a cell plate. As more vesicles fuse, the cell plate enlarges until it merges with the cell walls at the periphery of the cell. Enzymes use the glucose that has accumulated between the membrane layers to build a new cell wall. The Golgi membranes become parts of the plasma membrane on either side of the new cell wall.
G 0 Phase
Not all cells adhere to the classic cell cycle pattern in which a newly-formed daughter cell immediately enters the preparatory phases of interphase, closely followed by the mitotic phase. Cells in G 0 phase are not actively preparing to divide. The cell is in a quiescent (inactive) stage that occurs when cells exit the cell cycle. Some cells enter G 0 temporarily until an external signal triggers the onset of G 1 . Other cells that never or rarely divide, such as mature cardiac muscle and nerve cells, remain in G 0 permanently.
Contributions and Attributions
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44460/latest...ol11448/latest . License : CC BY: Attribution
- Boundless. Provided by : Boundless Learning. Located at : www.boundless.com//biology/de...itotic-spindle . License : CC BY-SA: Attribution-ShareAlike
- interphase. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/interphase . License : CC BY-SA: Attribution-ShareAlike
- sister chromatid. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/sister_chromatid . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Biology. November 4, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44460/latest...ol11448/latest . License : CC BY: Attribution
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44460/latest...ol11448/latest . License : CC BY: Attribution
- OpenStax College, Biology. October 21, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44460/latest...ol11448/latest . License : CC BY: Attribution
- karyokinesis. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/karyokinesis . License : CC BY-SA: Attribution-ShareAlike
- Boundless. Provided by : Boundless Learning. Located at : www.boundless.com//biology/de...on/cytokinesis . License : CC BY-SA: Attribution-ShareAlike
- centrosome. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/centrosome . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Biology. November 4, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44460/latest...ol11448/latest . License : CC BY: Attribution
- OpenStax College, The Cell Cycle. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44460/latest...e_10_02_02.png . License : CC BY: Attribution
- OpenStax College, The Cell Cycle. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44460/latest...e_10_02_03.jpg . License : CC BY: Attribution
- OpenStax College, The Cell Cycle. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44460/latest...e_10_02_04.jpg . License : CC BY: Attribution
Key Points
- During prophase, the nucleus disappears, spindle fibers form, and DNA condenses into chromosomes ( sister chromatids ).
- During metaphase, the sister chromatids align along the equator of the cell by attaching their centromeres to the spindle fibers.
- During anaphase, sister chromatids are separated at the centromere and are pulled towards opposite poles of the cell by the mitotic spindle.
- During telophase, chromosomes arrive at opposite poles and unwind into thin strands of DNA, the spindle fibers disappear, and the nuclear membrane reappears.
- Cytokinesis is the actual splitting of the cell membrane; animal cells pinch apart, while plant cells form a cell plate that becomes the new cell wall.
- Cells enter the G 0 (inactive) phase after they exit the cell cycle when they are not actively preparing to divide; some cells remain in G 0 phase permanently.
Key Terms
- karyokinesis : (mitosis) the first portion of mitotic phase in which division of the cell nucleus takes place
- centrosome : an organelle near the nucleus in the cytoplasm of most organisms that controls the organization of its microtubules and gives rise to the mitotic spindle
- cytokinesis : the second portion of the mitotic phase in which the cytoplasm of a cell divides following the division of the nucleus


6.11: Chapter Glossary and References
Chapter Glossary of Key Terms
Animism - Is the belief that all natural objects, the universe and important natural events all possess an individual spirit.
Ayahuasca - A traditional South American plant mixture made from the Banisteriopsis caapi vine combined with a variety of DMT containing plants, which is capable of producing altered states of consciousness.
Ideology - A system of ideas and ideals or manner of thinking which are characteristics of a group, social class, or individual.
Doctrine - belief or set of beliefs held and taught by a church, political party, or other group.
Myth - a commonly held but false belief; misconception. "Product of a man's emotion and imagination, acted upon by his surroundings." -E. Clodd, Myths and Dreams (1885)
Similarity Magic (Imitative Magic) - magic in which an object, act, etc. that is similar to a desired goal can be used to influence the outcome.
Peyote - A rare cactus found in Mexico containing the chemical mescaline which induces hallucinogenic experiences if ingested properly. Peyote has historically been ritualistically used in many indigenous cultures.
Exclusivism - This is the view that ones own religion is inerrant and all others are in error.
Anthropomorphism - Giving animals, plants, and other non-living objects human traits and personality. For example, how people say that plants are happy to be watered yet show no emotion, people would give traits that are exclusively human to things that are not human.
Canonization - the act when a Christian church declares that a person who has died was a saint, and said person is added to the list of recognized saints after an investigation of two miracles (one during the person’s life and the second after their death)
Rite of Passage - A life cycle ritual that marks a person's transition from one social state to another
Unity of Consciousness - The belief that you and a supernatural power are united in some symbolic way.
Spirituality - The quality or fact of relating to the spirit or soul; being spiritual
Shaman - a person regarded as having access to, and influence in, the world of good and evil spirits
Contagious Magic - The idea that any item that once was connected to a person’s body is still linked to them, so you can affect the person by effecting an item that was once connected to that person.
References
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p. 217 Schultz & Lavenda
-
Cultural Anthropology: Asking Questions About Humanity, Oxford University Press, 2015.
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William Harris Middlebury College. http://community.middlebury.edu/~harris/SubIndex/greekmyth.html
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Encyclopedia Brittanica. http://www.britannica.com/EBchecked/topic/600496/totemism
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Cotterell 2000
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Kappler http://digital.library.okstate.edu/KAPPLER/Vol2/Toc.htm
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Coleman, John A. S.J. "Conclusion: after sainthood", in Hawley, John Stratton, ed. Saints and Virtues Berkeley: University of California Press, 1987. pp 214-217
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Schultz, Emily A., and Robert H. Lavenda. Cultural Anthropology. 7th ed. New York: Oxford P, 2009.
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Furst, 2003, 18-24
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Linton, Ralph and Adelin Linton 1950 Halloween through twenty centuries New York, Schuman | http://www.worldcat.org/oclc/850555?tab=details
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http://www.trinity.edu/org/tricksters/trixway/current/Vol%201/Vol%201_1/Tstocker.html
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Fadiman, Anne. The Spirit Catches You and You Fall Down: A Hmong Child, Her American Doctors, and the Collision of Two Cultures. New York: Farrar, Straus, and Giroux, 1997. Print.
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[1] , Ember, Carol R., Christina Carolus. 2017. “Altered States of Consciousness” in C. R. Ember, ed. Explaining Human Culture. Human Relations Area Files http://hraf.yale.edu/ehc/summaries/altered-states-of-consciousness .
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The camphor flame By Christopher John Fuller
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Kasulis, Thomas P.; Aimes, Roger T.; Dissanayake, Wimal (1993). Self as Body in Asian Theory and Practice . State University of New York Press. 104. ISBN 079141079X .
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Dr. C. George Boeree, Shippensburg University, Introduction to Buddhism. http://webspace.ship.edu/cgboer/buddhaintro.html
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Dr. C. George Boeree, Shippensburg University, Introduction to Buddhism. http://webspace.ship.edu/cgboer/buddhaintro.html
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Dr. C. George Boeree, Shippensburg University, Introduction to Buddhism. http://webspace.ship.edu/cgboer/buddhaintro.html
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http://www.buddhanet.net/e-learning/buddhistworld/about-pilgrim.htm
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B.A Robinson. http://www.religioustolerance.org/buddhism.htm
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Hall, Alana. Japanese/Chinese language student, 3rd Year.
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A.C. Underwood, Shintoism: The Indigenous Religion of Japan
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McBennett, Mark. "Shinto." JapanZone. Japan Zone. 29 Apr 2009 < http://www.japan-zone.com/omnibus/shinto.shtml >.
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Authors, Contributors. "Belief and Practice." Encyclopedia of Shinto. 2006. Kokugakuin University. 29 Apr 2009 < http://eos.kokugakuin.ac.jp/modules/xwords/ >.
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http://www.jewishvirtuallibrary.org/jsource/Judaism/holiday4.html
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Folk, Holly. "Introduction to Religious Studies." Western Washington University, Bellingham. apr 2009. Performance.
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Brown, Lindsey Personal experience learned from attending Sunday school during grade school.
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Amplified Bible. http://www.biblegateway.com/passage/?search=matthew%205:17-48
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http://www.biblegateway.com/passage/?search=Romans%2013:10;&version=45 ;
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Kennedy, Kathleen. "Protestantism." Protestatism. Western Washington University, Bellingham. Jan. 2009.
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Encyclopædia Britannica. http://www.britannica.com/EBchecked/topic/24861/Anglicanism
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David Lloyd. I was part of the Episcopal Diocese of Olympia for 18 years.
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Aziz Sheikh, Radcliff Publishing 2000. http://books.google.com/books?hl=en&lr=&id=JQwlR3tu3LYC&oi=fnd&pg=PA17&dq=pillars+islam+shahada&ots=iUBDOQbYbE&sig=N17_aO1Vpe4viQIjF6COtsdo4pw#PPA18,M1
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Rippin, Andrew, and Jan Knappert. Textual Sources for the Study of Islam. 1990 ed. Chicago: Chicago Press, 1986. Print.
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Esposito, John L. Islam: The Straight Path. 3rd ed. New York: Oxford University Press, 1988. Print.
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B.A. Robinson. http://www.religioustolerance.org/agnostic.htm
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The Jonestown Massacre - http://www.huffingtonpost.com/adst/the-jonestown-massacre_b_8592338.html
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Perkins, Rodney.(1997) Cosmic Suicide: The Tragedy and Transcendence of Heaven's Gate
Wigoder, Geoffrey. "Mourning."The New Encyclopedia of Judaism. 2nd ed. New York University Press. 2002.
Turpin, Solvieg A. 1994 Shamanism and Rock Art in North America. TX. University of Texas at Austin. p. 9-24
Turpin, Solvieg A. 1994 Shamanism and Rock Art in North America. TX. University of Texas at Austin. p. 5
Turpin, Solvieg A. 1994 Shamanism and Rock Art in North America. TX. University of Texas at Austin p. 4
Schultz, Emily A. and Lavenda, Robert H. 2009 Cultural Anthropology: A Perspective on the Human Condition. 7th Edition. NY. Oxford University Press. p. 211
“Hajj.” The Columbia Encyclopedia, 6th ed. New York: Columbia University Press, 2001–07. www.bartleby.com/65/. February 19, 2009.
"pilgrimage." Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 19 Feb. 2009
Colin Wilson. 1996. Atlas of Holy Places & Sacred Sites. DK Adult. p. 29.
Karen Armstrong (2000,2002). Islam: A Short History. pp. 10–12.
"Muhammad." Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 19 Feb. 2009
Clarifying Christianity; What is Baptism? 1998. 19 Feb. 2009 < http://www.clarifyingchristianity.com/get_wet.shtml >
Fairchild, Mary. “What is Communion and Why Do Christians Observe Communion?”
Emperor Constantine. 19 Feb. 2009 < http://www.earlychurch.org.uk/constantine.php >
The Christian Empire: 313-476. United Methodist Women in Worship. 19 Feb. 2009 < http://gbgm-umc.org/UMW/bible/cea.stm >
Cole, Ethan. “China’s Crackdown on Christians Worsens”. The Christian Post 7 Feb. 2007. Feb 19 2007http://www.christianpost.com/Intl/Persecution/2008/02/china-s-crackdown-on-christians-worsens-07/index.html
"Anubis," Microsoft® Encarta® Online Encyclopedia 2008 < http://encarta.msn.com > © 1997-2008 Microsoft Corporation.
Scott, David. "Anubis". InterCity Oz. Inc. © 2000-2004. Feb 26 < http://www.touregypt.net/godsofegypt/anubis.htm >
Whitney. "Egyptian Afterlife". Hubpages Inc, © 2009. Feb 26 < http://hubpages.com/hub/Egyptian-Mythology-Afterlife >
Meyerhoff, Barbara, Linda A. Camino and Edith Turner. Rites of Passage...An Overview. In Encyclopedia of Religion. Edited by Mircea Eliade, Vol. 12. 380-387.
Sanyika, Dadisi. Gang Rites and Rituals of Initiation. In Crossroads: The Quest for Contemporary Rights of Passage. Edited by Mahdi, Louis Carus, Nancy Gever Christopher and Michael Meade. La Salle, IL. Open Court. 1996
Cotterell, Arthur 2000. Myths & Legends . London: Marshall Editions Ltd.
Frazer, James 2003 Golden Bough: A Study in "Magic and Religion" Kessinger Publishing
Kessler, Gary (2007). Voices of Wisdom: A Multicultural Philosophy Reader. Sixth Edition. pp. 30–36
Gautama Siddhartha, March 4, 2009
http://www.answers.com/topic/anthropomorphism
Wenner, Sara. “Basic Beliefs of Islam.” Minnesota State University: Mankato. 2001. 28 Feb. 2009 < http://www.mnsu.edu/emuseum/cultural/religion/islam/beliefs.html >.
“Islam.” Gale Virtual Reference Library. 2007. 5 Mar. 2009 < http://go.galegroup.com >.
Sherman, Daniel (2008). "Pastor Qualifications." < http://www.my-pastor.com/pastor-qualifications.html > (March 8, 2009)
James, Paul E. "Ritual And Religion." Anthropology 201. Western Washington University, Bellingham. 2009.
Hefner, Alan; Guimaraes,Virgilio. "Animism" March 5, 2008 < http://www.themystica.com/mystica/articles/a/animism.htm >
Harvey, Graham. "Animism; Respecting the Living World" 2006. New York: Columbia University Press.
Brown, Karen MacCarthy. "Mama Lola: A Vodou Priestess in Brooklyn" 1991, University of California Press, Berkeley and Los Angeles, California.
Henderson, Bobby. "Church of the Flying Spaghetti Monster" 9 Mar 2009 < http://www.venganza.org >
"Flying Spaghetti Monster" 9 Mar 2009
"Anthropology of religion: Common elements of religion." Palomar College. Palomar College. 8 Mar 2009 < http://anthro.palomar.edu/religion/rel_2.htm >.
"Agnostics and Agnosticism:Uncertainty about whether God exists." Religious Tolerance. Religious Tolerance. 9 Mar 2009 < http://www.religioustolerance.org/agnostic.htm >
<ref>Religions of the Ancient world https://books.google.com/books?hl=en&lr=&id=uvtebmqZZDYC&oi=fnd&pg=PA17&dq=monotheism+and+polytheism&ots=SUpIYAfZ0K&sig=D_8U8IG0P2Abad16vVSkVfMMf2U#v=onepage&q=monotheism%20and%20polytheism&f=false <ref>
-
Fadiman, Anne. The Spirit Catches You and You Fall Down: A Hmong Child, Her American Doctors, and the Collision of Two Cultures. New York: Farrar, Straus, and Giroux, 1997. Print.


4.3: Enzyme Catalysis and Kinetics
-
- 4.3.1: Introduction
- In this chapter, we look at the properties and mechanism of action of enzymes. These include allosteric change (induced fit, enzyme regulation), energetic events (changes in activation energy), and how enzymes work in open and closed (experimental) systems. Any catalyst, by definition, accelerates a chemical reaction. But enzymes and inorganic catalysts differ in important ways (blue and red in the table below).
-
- 4.3.2: Enzymes
- By 1941, their studies correlating mutations with enzyme deficiencies in Neurospora crassa (bread mold) and Drosophila melanogaster led George Beadle and Edward Tatum to propose the one-gene/one-enzyme hypothesis in 1941. In 1958, they shared Nobel Prize in Physiology and Medicine for this work.
Thumbnail: diagram showing the induced fit model in enzymes (Public Domain; LadyofHats ).


5.2: Introduction to Punctuation
What you’ll learn to do: analyze the use of punctuation marks
There are a few more important pieces of punctuation we should learn about in order to be more effective in our writing. These little marks can often be the cause of heartache and headaches. Errors in punctuation can often have unintended meanings. For example, consider the difference the comma makes in the following sentences:
- Let’s eat, Grandpa.
- Let’s eat Grandpa.
The comma in the first sentence indicates that you are addressing Grandpa and telling him that you would like to eat. The lack of a comma in the second sentence makes this sentence sound like you are considering cannibalism. That little punctuation mark makes a big difference in what you are trying to say and can lead to some interesting misunderstandings if not used correctly.
However, punctuation doesn’t exist simply to cause problems; in fact, it was created to help communication. These marks were invented to guide readers through passages—to let them know how and where words relate to one another. When you learn the rules of punctuation, you equip yourself with an extensive toolset, so you can better craft language to communicate the exact message you want.
As we mentioned at the beginning of this module, different style guides have slightly different rules for grammar. This is especially true when it comes to punctuation. This section will cover the MLA rules for punctuation, but we’ll also make note of rules from other styles when they’re significantly different.
Contributors and Attributions
- Outcome: Punctuation. Provided by : Lumen Learning. License : CC BY: Attribution


6.3: Intermolecular Forces
- Describe the types of intermolecular forces possible between atoms or molecules in condensed phases (dispersion forces, dipole-dipole attractions, and hydrogen bonding)
Forces between Molecules
Intra molecular forces are those within the molecule that keep the molecule together, for example, the bonds between the atoms. However, there are also forces of attraction that can occur between molecules. Inter molecular forces (IMFs) are the attractions between molecules, which determine many of the physical properties of a substance. Figure \(\PageIndex{4}\) illustrates these different molecular forces. The strengths of these attractive forces vary widely, though usually the IMFs between small molecules are weak compared to the intramolecular forces that bond atoms together within a molecule.


10.5: Tessellations
- Apply translations, rotations, and reflections.
- Determine if a shape tessellates.
The illustration shown above (Figure
) is an unusual pattern called a Penrose tiling. Notice that there are two types of shapes used throughout the pattern: smaller green parallelograms and larger blue parallelograms. What's interesting about this design is that although it uses only two shapes over and over, there is no repeating pattern.In this section, we will focus on patterns that do repeat. Repeated patterns are found in architecture, fabric, floor tiles, wall patterns, rug patterns, and many unexpected places as well. It may be a simple hexagon-shaped floor tile, or a complex pattern composed of several different motifs. These two-dimensional designs are called regular (or periodic) tessellations . There are countless designs that may be classified as regular tessellations, and they all have one thing in common—their patterns repeat and cover the plane.
We will explore how tessellations are created and experiment with making some of our own as well. The topic of tessellations belongs to a field in mathematics called transformational geometry, which is a study of the ways objects can be moved while retaining the same shape and size. These movements are termed rigid motions and symmetries .
A good place to start the study of tessellations is with the work of M. C. Escher. The Dutch graphic artist was famous for the dimensional illusions he created in his woodcuts and lithographs, and that theme is carried out in many of his tessellations as well. Escher became obsessed with the idea of the “regular division of the plane.” He sought ways to divide the plane with shapes that would fit snugly next to each other with no gaps or overlaps, represent beautiful patterns, and could be repeated infinitely to fill the plane. He experimented with practically every geometric shape imaginable and found the ones that would produce a regular division of the plane. The idea is similar to dividing a number by one of its factors. When a number divides another number evenly, there are no remainders, like there are no gaps when a shape divides or fills the plane.
Escher went far beyond geometric shapes, beyond triangles and polygons, beyond irregular polygons, and used other shapes like figures, faces, animals, fish, and practically any type of object to achieve his goal; and he did achieve it, beautifully, and left it for the ages to appreciate.
M.C. Escher: How to Create a Tessellation
The Mathematical Art of M.C. Escher
Tessellation Properties and Transformations
A regular tessellation means that the pattern is made up of congruent regular polygons, same size and shape, including some type of movement ; that is, some type of transformation or symmetry. Here we consider the rigid motions of translations, rotations, reflections, or glide reflections. A plane of tessellations has the following properties:
- Patterns are repeated and fill the plane.
- There are no gaps or overlaps. Shapes must fit together perfectly. (It was Escher who determined that a proper tessellation could have no gaps and no overlaps.)
- Shapes are combined using a transformation.
- All the shapes are joined at a vertex. In other words, if you were to draw a circle around a vertex, it would include a corner of each shape touching at that vertex.
- For a tessellation of regular congruent polygons, the sum of the measures of the interior angles that meet at a vertex equals
In Figure
, the tessellation is made up of squares. There are four squares meeting at a vertex. An interior angle of a square is \(90^{\circ}\) and the sum of four interior angles is \(360^{\circ}\). In Figure , the tessellation is made up of regular hexagons. There are three hexagons meeting at each vertex. The interior angle of a hexagon is \(120^{\circ}\), and the sum of three interior angles is \(360^{\circ}\). Both tessellations will fill the plane, there are no gaps, the sum of the interior angle meeting at the vertex is \(360^{\circ}\), and both are achieved by translation transformations. These tessellations work because all the properties of a tessellation are present.The movements or rigid motions of the shapes that define tessellations are classified as translations, rotations, reflections, or glide reflections. Let’s first define these movements and then look at some examples showing how these transformations are revealed.
Translation
A
translation
is a movement that shifts the shape vertically, horizontally, or on the diagonal. Consider the trapezoid
Suppose you have a hexagon on a grid as in Figure 10.105. Translate the hexagon 5 units to the right and 3 units up.
- Answer
-
The best way to do this is by translating the individual points . Once translated, the points become
Translate the hexagon with points \(A',\) \(B',\) \(C', \) \(D',\) \(E',\) \(F'\) 6 units down.
Rotation
The rotation transformation occurs when you rotate a shape about a point and at a predetermined angle. In Figure
, the triangle is rotated around the rotation point by and then translated 7 units up and 4 units over to the right. That means that each corner is translated to the new location by the same number of units and in the same direction.
We can see that
Figure
illustrates a tessellation begun with an equilateral triangle. Explain how this pattern is produced.- Answer
-
A rotation to the right or to the left around the vertex by six times, produces the hexagonal shape. The sixth rotation brings the triangle back to its original position. Then, a reflection up and another one on the diagonal will reproduce the pattern. When a shape returns to its original position by a rotation, we say that it has rotational symmetry.
Starting with the triangle in the figure shown, explain how the pattern on the right was achieved.
Reflection
A reflection is the third transformation. A shape is reflected about a line and the new shape becomes a mirror image. You can reflect the shape vertically, horizontally, or on the diagonal. There are two shapes in Figure . The quadrilateral is reflected horizontally; the arrow shape is reflected vertically.
Glide Reflection
The glide reflection is the fourth transformation. It is a combination of a reflection and a translation. This can occur by first reflecting the shape and then gliding or translating it to its new location, or by translating first and then reflecting. The example in Figure shows a trapezoid, which is reflected over the dashed line, so it appears upside down. Then, we shifted the shape horizontally by 6 units to the right. Whether we use the glide first or the reflection first, the end result is the same in most cases. However, the tessellation shown in the next example can only be achieved by a reflection first and then a translation.
An obtuse triangle is reflected about the dashed line, and the two shapes are joined together. How does the tessellation shown in Figure
materialize?- Answer
-
The new shape is reflected horizontally and joined with the original shape. It is then translated vertically and horizontally to make up the tessellation. Notice the blank spaces next to the vertical pattern. These areas are made up of the exact original shape rotated but with no line up the center. These rotated shapes are translated horizontally and vertically, and thus, the plane is tessellated with no gaps. This is an example of a glide reflection where the order of the transformations matters.
Explain how this tessellation of equilateral triangles could be produced.
Show how this tessellation (Figure
) can be achieved.- Answer
-
This is a tessellation that has one color on the front of the trapezoid and a different color on the back. There is a translation on the diagonal, and a reflection vertically. These are two separate transformations resulting in two new placements of the trapezoid. We can call this a combination of two transformations or a glide reflection.
How does this tessellation of the squares come about?
Interior Angles
The sum of the interior angles of a tessellation is \(360^{\circ}\). In Figure
, the tessellation is made of six triangles formed into the shape of a hexagon. Each angle inside a triangle equals \(60^{\circ}\), and the six vertices meet the sum of those interior angles, \(6\left(60^{\circ}\right)=360^{\circ}\).In Figure
, the tessellation is made up of trapezoids, such that two of the interior angles of each trapezoid equals and the other two angles equal . Thus, the sum of the interior angles where the vertices of four trapezoids meet equals .These tessellations illustrate the property that the shapes meet at a vertex where the interior angles sum to .
Tessellating Shapes
We might think that all regular polygons will tessellate the plane by themselves. We have seen that squares do and hexagons do. The pattern of squares in Figure
is a translation of the shape horizontally and vertically. The hexagonal pattern in Figure , is translated horizontally, and then on the diagonal, either to the right or to the left. This particular pattern can also be formed by rotations. Both tessellations are made up of congruent shapes and each shape fits in perfectly as the pattern repeats.We have also seen that equilateral triangles will tessellate the plane without gaps or overlaps, as shown in Figure
. The pattern is made by a reflection and a translation. The darker side is the face of the triangle and the lighter side is the back of the triangle, shown by the reflection. Each triangle is reflected and then translated on the diagonal.Escher experimented with all regular polygons and found that only the ones mentioned, the equilateral triangle, the square, and the hexagon, will tessellate the plane by themselves. Let’s try a few other regular polygons to observe what Escher found.
Do regular pentagons tessellate the plane by themselves (Figure
)?- Answer
-
We can see that regular pentagons do not tessellate the plane by themselves. There is a gap, a gap in the shape of a parallelogram. We conclude that regular pentagons will not tessellate the plane by themselves.
Do regular heptagons tessellate the plane by themselves?
Do regular octagons tessellate the plane by themselves (Figure
)?- Answer
-
Again, we see that regular octagons do not tessellate the plane by themselves. The gaps, however, are squares. So, two regular polygons, an octagon and a square, do tessellate the plane.
Do regular dodecagons (12-sided regular polygons) tessellate the plane by themselves?
Just because regular pentagons do not tessellate the plane by themselves does not mean that there are no pentagons that tessellate the plane, as we see in Figure
.Another example of an irregular polygon that tessellates the plane is by using the obtuse irregular triangle from a previous example. What transformations should be performed to produce the tessellation shown in Figure
?First, the triangle is reflected over the tip at point , and then translated to the right and joined with the original triangle to form a parallelogram. The parallelogram is then translated on the diagonal and to the right and to the left.
Naming
A tessellation of squares is named by choosing a vertex and then counting the number of sides of each shape touching the vertex. Each square in the tessellation shown in Figure
has four sides, so starting with square , the first number is 4, moving around counterclockwise to the next square meeting the vertex, square , we have another 4, square adds another 4, and finally square adds a fourth 4. So, we would name this tessellation a <IP_ADDRESS>.The hexagon tessellation, shown in Figure
has six sides to the shape and three hexagons meet at the vertex. Thus, we would name this a 6.6.6. The triangle tessellation, shown in Figure has six triangles meeting the vertex. Each triangle has three sides. Thus, we name this a <IP_ADDRESS>.3.3.Create a tessellation using two colors and two shapes.
- Answer
-
We used a parallelogram and an isosceles triangle. The parallelogram is reflected vertically and horizontally so that only every other corner touches. The triangles are reflected vertically and horizontally and then translated over the parallelogram. The result is alternating vertical columns of parallelograms and then triangles (Figure 10.131).
Figure
Create a tessellation using polygons, regular or irregular.
Check Your Understanding
1. What are the properties of repeated patterns that let them be classified as tessellations?
2. Explain how the using the transformation of a translation is applied to the movement of this shape starting with point \(A\).
3. Starting with the triangle with vertex \(B\), describe how the transformation in this drawing is achieved.
4.
5. Name the tessellation in the figure shown.


6.6: Saccharolipids, polyketides, and prenols
- Define and understand the basic structural features of saccharolipids, polyketides, and prenols.
- Define mono-, sesqui-, di-, and tri-terpenes and recognize isoprene units in terpenes, terpenoids, and steroids.
Saccharolipids
Saccharolipids are fatty acids linked to a saccharide (carbohydrate) backbone by linkages other than glycosidic linkages. They are compatible with membrane bilayers. For example, saccharolipid lipid A found in E. Coli is shown in the figure on the right.
Polyketides
Polyketides are a broad class of natural products derived from \(\beta\)-polyketones, i.e., compounds containing \(\ce{[-\!\!{\overset{\overset{\huge\enspace\!{O}}|\!\!|\enspace}{C}}\!\!-CH2{-}]_{n}}\) repeat units in their backbone or their reduced forms, such as \(\ce{[-\!\!\!\!\!{\overset{\overset{\huge\enspace\enspace{OH}}|}{C}}\!\!\!\!\!-CH2{-}]_{n}}\), and \(\ce{[-CH2-CH2{-}]_{n}}\). Polyketides are important in the pharmaceutical industry. They are used as antimicrobial, antiparasitic, and anticancer agents; some are toxins. About 20% of the top-selling medicines are polyketides. Some examples of medically important polyketide products are shown below.
Prenols
Prenols are synthesized from five-carbon isoprene precursors: isopentenyl pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP), as shown in Figure \(\PageIndex{1}\) (left). The five-carbon skeleton of isoprene units in these products can often be easily distinguished, as shown in by different color sections of some examples in Figure \(\PageIndex{1}\) (right). Since they contain a multiple of five \(\ce{C's}\) in their skeleton, they are also classified as monoterpens (10 \(\ce{C's}\)), sesquiterpenes (15 \(\ce{C's}\)), diterpenes (20 \(\ce{C's}\)), triterpenes ((30 \(\ce{C's}\)), and tetraterpenes (40 \(\ce{C's}\)). Terpenoids are modified terpenes that contain additional functional groups, usually oxygen functional groups as those shown in \(\PageIndex{1}\) (right).
.
Steroids -other lipids described later are derived from triterpene squalene, as illustrated in Figure \(\PageIndex{2}\).


12.3.2: Statistics are People
We must remember that behind every statistic are the people that these injuries and illnesses happened to. Lives are lost, or permanently changed. The ability to work, earn a living, or even physically move and perform activities of daily living (ADLs) is disrupted by non-fatal injuries and illnesses in the workplace. When people get hurt or sick enough from their job that they can no longer work, they end up with a permanent disability that often forces them to spend much more time and money getting treatment, and substantially affects their socioeconomic status and quality of life. Perhaps the biggest tragedy is that many of these incidents can be prevented with proper safety and health policies and procedures in place. When young workers are injured or killed on the job it is particularly tragic; a young life was cut short, or a young person must live with a disability for the rest of their lives.
The OSHA website has several such stories of preventable workplace injuries and deaths to young people. Teenagers working in a grain silo were caught and pulled into the grain, suffocating them - they were not wearing protective harnesses at the time. A young construction worker was cleaning a cement mixer, and got pulled in by the paddles, while a nearby coworker didn’t know how to shut it off. A teen performing routine pH testing on a swimming pool was electrocuted by the machinery and the wet concrete. Falls are the most common cause of injury and death on construction sites, and people often lose fingers or limbs when operating heavy machinery (OSHA, n.d.-b). While these are likely meant as cautionary tales, they also serve to personalize these incidents and give a voice to the victim. Workers are people, whose health and safety matters more than just the dollar amount of the worker’s compensation claim.


9.1: Production Budget
Learning Objectives
- Create a production budget
Once we get the sales budget prepared, you can see on the flow chart that the next budget we need to work on is the production budget. This budget is necessary to provide all of the details we need to prepare direct materials, direct labor and manufacturing overhead budgets that come next.
The production budget outlines the number of units that we need to produce to meet the requirements we put together in the sales budget. This information needs to be completed prior to moving forward. Without knowing how many of our products we need to make, it would be impossible to move forward with the remaining budgets!
So remember our sales numbers for Hupana Running Company from our sales budget. We plan to sell 2,000 pairs of shoes, evenly distributed between the four quarters of the year. Armed with this information, we can create our production budget.
We had 100 pairs of shoes in our finished goods inventory at the end of the previous year, so we can use that number as we start our production budget. We also want to always have at least 50 pair in our finished goods inventory at the end of each quarter, but would like to end the year with 150 pair in inventory to start the next year.
| Hupana Running Company Production Budget | |||||
|---|---|---|---|---|---|
| Quarter | Q1 | Q2 | Q3 | Q4 | Totals |
| Budgeted unit sales (pairs) | 500 | 500 | 500 | 500 | 2000 |
| Desired finished goods inventory | 50 | 50 | 50 | 150 | 300 |
| Total need | 550 | 550 | 550 | 650 | 2300 |
| Less beginning finished goods inventory | 100 | 50 | 50 | 50 | 250 |
| Required production units | 450 | 500 | 500 | 600 | 2050 |
So taking a look at our production budget, what do you notice?
Even though we intend to sell 2000 pairs of shoes this year, we are producing 2050! Why? Because we would like to have a larger ending inventory at the end of this year. This could be for a few reasons. Perhaps we anticipate higher sales in the first quarter, or maybe we want to have a plant shut down in the early part of the year. This higher ending finished goods inventory would allow us to cover those two situations.
Also notice, that in the first and fourth quarters, we are actually producing either fewer or more pairs of shoes than we intend to sell. This is to adjust for finished goods inventory.
Note: So Hupana Running Company is a manufacturer. What might be different if they were a merchandising company who simply purchased finished goods to sell? Well, instead of a production budget , they would have a merchandise purchases budget . It would be similar in layout to the production budget, but the wording would be different. Rather than a required production in units, we would simply have required purchases. Oh, and we could skip some of the additional budgets, like production, direct labor and manufacturing overhead! Why? Well, if we aren’t actually manufacturing anything, those budgets aren’t needed. A merchandising company is a bit easier to budget for, but let’s keep plugging away at our manufacturing company!Now let’s practice!
Practice Questions